A rotor in its simplest form includes two primary parts, a rotatable disk and multiple blades mounted on the disk in a certain pattern with respect to the disk center. Rotors are used in two configurations in many machines: using the rotation of blades of a powered rotor to propel a gas or liquid and using a moving gas or liquid to rotate the rotor which in turn generates driving power. For example, a fan uses the rotation of blades of an electrically driven rotor to cause air circulation; a motor boat uses the rotation of blades of a fuel-powered rotor to propel water, thus causing the boat to move; a turbine engine implements complex rotors to compress inlet air to generate a high-pressure air flow to a combustion chamber and to use a portion of the static and kinetic energy of the air flow from the combustion chamber for driving an air compressor.
However implemented, blades of a rotor interact with a fluid in gaseous or aqueous form and exhibit complex dynamic behaviors. There have been tremendous efforts in researching the aerodynamic and mechanical properties of blades and the blade spatial distribution around the center disk. The blade design and blade spatial distribution for rotors used in air compressors and turbines for aircraft engines are particularly critical because these rotors operate at high rotational speeds (e.g., up to 8000 rpm or higher) in gas flows of high pressure variations, high-temperature (e.g., up to 2000.degree. F. or higher), and high fluid speeds (e.g., up to 2000 ft/sec or higher).
One technical issue in designing a rotor is the blade spatial distribution. Blades of a rotor not only interact with the surrounding fluid but also are dynamically coupled to one another through their interaction with the fluid. This dynamic interaction results in complex dynamic behaviors of the blades. A properly designed blade spatial distribution can prolong the lifetime of blades and reduce failure of blades.
Ideal blades in a rotor are identical to one another in all respects of a blade, such as shape, dimension, material composition, and material uniformity, etc. In this ideal case, any blade behaves exactly like any other blade. Such an ideal rotor is said to be "tuned".
However, manufacturing processes inherently produce is small variations in blades. This causes mistuning of the blades. Variations from one blade to another in a rotor may also be caused by wear through a period of operation. It has been recognized that such mistuned blades, even if within the manufacturing tolerances, can cause instabilities in the rotor operation and introduce adverse forced responses of the blades with associated high cycle fatigue. Both instabilities and high cycle fatigue can ultimately lead to failure of a turbine engine.
Many techniques have been used to analyze the effects of mistuned turbomachines. See, for example, Bendiksen, "Flutter of mistuned turbomachinery rotors," ASME Journal of Engineering for Gas Turbines & Power, vol. 106, pp. 25-33 (1984); Dye and Henry, "Vibration amplitudes of compressor blades resulting from scatter in blade natural frequencies," ASME Journal Engineering for Power, Vol. 91, pp. 182-188 (1969); Srinivasan and Frye, "Effects of mistuning on resonant stresses of turbine blades," in Structural Dynamic Aspects of Bladed Disk Assemblies, 1976; and Whitehead, "Effect of mistuning on the vibration of turbomachine blades induced by wakes," Journal Mechanical Engineering Science, Vol. 8, pp. 15-21 (1966).